Editing Network analysis (electrical circuits) (section)

====Piecewise linear method====
In this method, the transfer function of the non-linear device is broken up into regions.  Each of these regions is approximated by a straight line.  Thus, the transfer function will be linear up to a particular point where there will be a discontinuity.  Past this point the transfer function will again be linear but with a different slope.

A well known application of this method is the approximation of the transfer function of a pn junction diode.  The transfer function of an ideal diode has been given at the top of this (non-linear) section.  However, this formula is rarely used in network analysis, a piecewise approximation being used instead.  It can be seen that the diode current rapidly diminishes to -I<sub>o</sub> as the voltage falls.  This current, for most purposes, is so small it can be ignored.  With increasing voltage, the current increases exponentially.  The diode is modelled as an open circuit up to the knee of the exponential curve, then past this point as a resistor equal to the [[bulk resistance]] of the semiconducting material.

The commonly accepted values for the transition point voltage are 0.7V for silicon devices and 0.3V for germanium devices.  An even simpler model of the diode, sometimes used in switching applications, is short circuit for forward voltages and open circuit for reverse voltages.

The model of a forward biased pn junction having an approximately constant 0.7V is also a much used approximation for transistor base-emitter junction voltage in amplifier design.

The piecewise method is similar to the small signal method in that linear network analysis techniques can only be applied if the signal stays within certain bounds.  If the signal crosses a discontinuity point then the model is no longer valid for linear analysis purposes.  The model does have the advantage over small signal however, in that it is equally applicable to signal and dc bias. These can therefore both be analysed in the same operations and will be linearly superimposable.